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Effective Ramsey Theorems in the Projective Hierarchy

Kechris, Alexander S. (1982) Effective Ramsey Theorems in the Projective Hierarchy. In: Proceedings of the Herbrand Symposium. Studies in Logic and the Foundations of Mathematics. No.107. Elsevier , Amsterdam, pp. 179-187. ISBN 9780444864178.

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This chapter discusses Ramsey theorems that are effective in the projective hierarchy. The application of Q-theory is quite elementary; it will bring out some of its essential ideas and methods that can be basic ingredients in more elaborate uses and applications of this theory. The chapter proves the main theorem and discusses results related results on Δ^1_(2n+l)- and Q_(2n+l)- encodability, and discusses some related open problems. One of the proof uses Mathias forcing over an appropriate inner model of ZFC.

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Additional Information:© 1982 North-Holland Publishing Company. Published by Elsevier B.V. The author is an A. P. Sloan Foundation Fellow. NSF Grant MCS79-20465. Research partially supported by NSF Grant MCS79-20465.
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MathSciNet ReviewMR0757028
Series Name:Studies in Logic and the Foundations of Mathematics
Issue or Number:107
Record Number:CaltechAUTHORS:20130531-145645449
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Official Citation:Alexander S. Kechris, Effective Ramsey Theorems in the Projective Hierarchy, In: J. Stern, Editor(s), Studies in Logic and the Foundations of Mathematics, Elsevier, 1982, Volume 107, Pages 179-187, ISSN 0049-237X, ISBN 9780444864178, 10.1016/S0049-237X(08)71883-4. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38737
Deposited By: Ruth Sustaita
Deposited On:31 May 2013 22:22
Last Modified:09 Nov 2021 23:39

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